What is the extreme f(x)=f(x)=5+54x-2x^3,0<= x<= 4 ?

The extreme f(x)=f(x)=5+54x-2x^3,0<= x<= 4 is Minimum(0,5),Maximum(3,113),Minimum(4,93)

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extreme f(x)=f(x)=5+54x-2x^3,0<= x<= 4

extreme points

f (x) = f (x) = 5 + 54 x - 2 x^{3}, 0 \leq x \leq 4

Minimum (0, 5), Maximum (3, 113), Minimum (4, 93)

Solution steps

Find the critical points:

x = 0, x = 3, x = 4

Domain of

5 + 54 x - 2 x^{3}, 0 \leq x \leq 4 : 0 \leq x \leq 4

Find intervals:

Increasing

: 0 < x < 3,

Decreasing

: 3 < x < 4

Plug the extreme point

x = 0

into

5 + 54 x - 2 x^{3} \Rightarrow y = 5

Minimum (0, 5)

Plug the extreme point

x = 3

into

5 + 54 x - 2 x^{3} \Rightarrow y = 113

Maximum (3, 113)

Plug the extreme point

x = 4

into

5 + 54 x - 2 x^{3} \Rightarrow y = 93

Minimum (4, 93)

Minimum (0, 5), Maximum (3, 113), Minimum (4, 93)

f (x) = 82 x^{2} + 180 x + 100

P (x, y) = x^{2} + y^{2} + 16 x - 16 y

f (x) = - 0.001 x^{2} + 9 x - 1296

f (x) = \frac{( 500 + 500 \cdot x )}{1 + 0.04 \cdot x ^{2}}

\frac{( x ^{2} + 2 )}{( x ^{2} - 16 )}

What is the extreme f(x)=f(x)=5+54x-2x^3,0<= x<= 4 ?
The extreme f(x)=f(x)=5+54x-2x^3,0<= x<= 4 is Minimum(0,5),Maximum(3,113),Minimum(4,93)